#### Do you have a question? Post it now! No Registration Necessary

**posted on**

- Richard Rasker

March 11, 2008, 1:39 pm

Hello,

The problem seems simple: I have a circuit on 24V DC I'm trying to protect

with a 250mA SMD fuse(*) in the supply line. The circuit itself needs some

50mA at most, and several PCB tracks and components would constitute a fire

hazard at substantially more than a few hundred mA, so a 250mA fuse would

be ideal.

*: See

http://nl.farnell.com/1123250/electrical/product.us0?sku=BUSSMANN-3216FF250-R

The trouble is that the fuse often blows upon switching on the supply

voltage, probably due to the inrush current into a 220uF supply capacitor

behind the fuse.

The fuse has a typical I^2t value of 0.000084, and a cold series resistance

of 4 ohms (including wiring etcetera), so one would expect a worst case

inrush current of 24/46A% at the moment of switching on; at a constant 6A,

charge time is some 0.9 milliseconds -- and as the datasheet specifies a

hold time of 1 millisecond at only 1.3A, it's not surprising that the fuse

should blow.

The point is, however, that this 6A very rapidly diminishes as the voltage

over the capacitor rises, following an e-power curve, so the actual I^2t

load on the capacitor is lower.

First the theory question: Is there an easy calculation providing a link

between a diminishing inrush current and an I^2t value?

The practical question is of course how to solve this particular problem.

There appear to be no slow fuses in 1206 SMD cases, so I guess I'll have to

resort to using a bigger type of fuse. I could also use a smaller capacitor

(down to some 22uF) -- but the inrush current would stay the same, only

with a correspondingly shorter charge time. So I'd need really need to know

(calculate?) what happens to the fuse in these cases.

But perhaps someone can come up with another good suggestion?

And oh: I have done some experiments with SMD resistors, but these turn out

to be amazingly resilient to excess power -- I had a 1.5 ohm 1206 resistor

desoldering itself after a minute or so of carrying almost 1 ampere of

current, with only a minor increase in resistance. And at 2 amperes, it

glowed red for several seconds before failing -- but by then I guess the

charred PCB could take over the role of conductor.

Thanks in advance,

Richard Rasker

The problem seems simple: I have a circuit on 24V DC I'm trying to protect

with a 250mA SMD fuse(*) in the supply line. The circuit itself needs some

50mA at most, and several PCB tracks and components would constitute a fire

hazard at substantially more than a few hundred mA, so a 250mA fuse would

be ideal.

*: See

http://nl.farnell.com/1123250/electrical/product.us0?sku=BUSSMANN-3216FF250-R

The trouble is that the fuse often blows upon switching on the supply

voltage, probably due to the inrush current into a 220uF supply capacitor

behind the fuse.

The fuse has a typical I^2t value of 0.000084, and a cold series resistance

of 4 ohms (including wiring etcetera), so one would expect a worst case

inrush current of 24/46A% at the moment of switching on; at a constant 6A,

charge time is some 0.9 milliseconds -- and as the datasheet specifies a

hold time of 1 millisecond at only 1.3A, it's not surprising that the fuse

should blow.

The point is, however, that this 6A very rapidly diminishes as the voltage

over the capacitor rises, following an e-power curve, so the actual I^2t

load on the capacitor is lower.

First the theory question: Is there an easy calculation providing a link

between a diminishing inrush current and an I^2t value?

The practical question is of course how to solve this particular problem.

There appear to be no slow fuses in 1206 SMD cases, so I guess I'll have to

resort to using a bigger type of fuse. I could also use a smaller capacitor

(down to some 22uF) -- but the inrush current would stay the same, only

with a correspondingly shorter charge time. So I'd need really need to know

(calculate?) what happens to the fuse in these cases.

But perhaps someone can come up with another good suggestion?

And oh: I have done some experiments with SMD resistors, but these turn out

to be amazingly resilient to excess power -- I had a 1.5 ohm 1206 resistor

desoldering itself after a minute or so of carrying almost 1 ampere of

current, with only a minor increase in resistance. And at 2 amperes, it

glowed red for several seconds before failing -- but by then I guess the

charred PCB could take over the role of conductor.

Thanks in advance,

Richard Rasker

--

http://www.linetec.nl /

http://www.linetec.nl /

Re: Fuse/supply capacitor calculations

At only 50 mA, maybe you could use a resistor

___and___a fuse, along with

cutting the capacitor by a factor of ten, if you can actually stand

that. Seems like a much smaller capacitor could also have a higher

ESR, and so a lower peak current.

--

John

John

Re: Fuse/supply capacitor calculations

Seehttp://nl.farnell.com/1123250/electrical/product.us0?sku=BUSSMANN-321 ...

About the theoretical part, it's an RC circuit, and the resistor

(fuse) voltage is

V * e^(-t/(RC)). (The original 24V times a factor that goes from 1 to

zero as time goes from zero to infinity).

The current is that divided by the resistance R. The I^2t should be

integral ( (V/R*e^(-t/RC))^2 dt, t = 0 to infinity).

With V = 24, R = 4ohms, C = 220uF, this is

int( (24V/4ohms

*** e^(-t/(4ohm***220uF)) ^2 dt, t = 0 to infinity),

which my TI-89 says is .01584 amps squared * seconds. Or square amps?

With 22 uF, it's .001584. With 220 uF and an additional 4 ohm resistor

(total 8 ohms), you get .00792 for I^2T. With 22 uF and 8ohms total,

you get 0.000792. The value scales linearly with capacitance, and non-

linearly with resistance.

This ignores any change in resistance of the parts due to heating,

which would depend on their physical description.

--

John

John

Re: Fuse/supply capacitor calculations

protect

some

fire

Seehttp://nl.farnell.com/1123250/electrical/product.us0?sku=BUSSMANN-321 ...

resistance

6A,

fuse

voltage

to

capacitor

know

out

resistor

And I did something wrong - I forgot to multiply by t in the integral

of I^2T. The result is independent of resistance, and depends only on

the capacitance, which makes sense, since the capacitance charges as

current times time.. The higher the R, the lower the current but the

longer the time. The value of I^2T for 24 V and 220 uF is 7*10^-6.

So, with the same capacitor but a larger series resistance, the fuse

is able to dissipate the heat, but the energy passed through is the

same.

The only thing worse than being wrong is staying wrong. Sorry I can't

help on the theoretical question!

--

John

John

Re: Fuse/supply capacitor calculations

protect

some

fire

would

Seehttp://nl.farnell.com/1123250/electrical/product.us0?sku=BUSSMANN-321 ...

capacitor

resistance

6A,

a

fuse

voltage

I^2t

link

problem.

have to

capacitor

know

turn out

resistor

the

On the off chance that anyone is still following my string of self-

replies, I have to correct myself yet another time. Integration across

time is already multiplying by time, and my original calculation of

I2T, and the formulas, were correct. The total I*t to charge a

capacitor is fixed, but the I^2*t isn't.

I apologize to everyone for my dithering.

--

John

John

Re: Fuse/supply capacitor calculations

...

[snip]

I especially chose a low ESR cap of a relatively high value because it's

hooked up to an SMPS, but I think I can get away with 22uF.

I suspected out so much, although I hadn't started on calculations yet.

I'd say amps squared seconds. I think I'll do the math myself as well, if

only to brush up on my math skills, but this 0.016 is indeed two hundred

times higher than the specified I^2t value of the fuse. This, by the way,

is at least an order of magnitude lower than the I^2t of regular glass

fuses, even the fast ones (which also explains why I never ran into this

problem before, having built hundreds of fuse-protected circuits ...)

Well, thanks a lot for your elaborate reply (and all the followups :-).

I'll probably just take a slower type of fuse, perhaps combined with a

smaller capacitor.

Thanks again, best regards,

Richard Rasker

--

http://www.linetec.nl /

http://www.linetec.nl /

Re: Fuse/supply capacitor calculations

You're welcome. I note that Wimpie's reply is exactly right (and

simpler), with R*C as the 36% discharge time - it's exactly what that

integral evaluates to. It can also be expressed as

.5

*** V^2 ***C/R, which shows the direct linear dependence on C and

inverse on R.

--

John

John

Re: Fuse/supply capacitor calculations

Hi Richard,

I2t = 0.5

***(Ipeak)^2***(36% decay time).

So faster charging reduces the charging time, but in the end

increases I2t. I assume that you switch from a low output impedance

source. Is there any room/space/budget to add a current limiter (that

"consumes" just 100mV under normal use), or a dV/dt limitation?

Best regards,

Wim

PA3DJS

www.tetech.nl

Re: Fuse/supply capacitor calculations

[snip]

With the current's influence squared and the time factor linear, this means

that an increased current is far worse than a longer charging time.

The 24 volts supply voltage is from a big ship's batteries, capable of

delivering a few thousand amps, so yes, I'd think we can call that a low

impedance source :-)

There is room for a current limiter, but I think the low-tech solution of

simply using a slower fuse is better.

I think I'll also run some tests with several types of fuses and several

capacitor values, having a relay switch between charging and discharging

the capacitor through the fuse once a second for an hour or so. This should

give some more information on a practical combination of values. If

anything interesting comes out of this, I'll post it here.

Thanks for your reply, best regards,

Richard Rasker

--

http://www.linetec.nl /

http://www.linetec.nl /

Re: Fuse/supply capacitor calculations

Hi Richard,

Did you also take into account that when the switching action occurs

frequently the expected life of your electrolytic capacitor may reduce

significantly.

Depending on the inductance of the feed line and resistive losses

(probably low), you may also get a voltage spike across the input

electrolytic capacitor (the better the capacitor, the higher the

spike). You might run a simplified (spice) simulation to see the

effect for yourself.

Some months ago a client had a similar fuse problem. He also wanted to

use an SMT fuse (space problem). I2t rating of the SMT fuses were far

too low (so they use a glass fuse now).

Best regards,

Wim

PA3DJS

www.tetech.nl

Re: Fuse/supply capacitor calculations

The circuit is switched on and off a few times a week at most, so I don't

think this will be a serious problem.

I couldn't fit in a glass fuse, but inserting a series resistor of a dozen

ohms fixed it for me -- the resulting extra voltage drop is no problem, and

even after multiple thousand on/off cycles (with a 0.5Hz oscillator and a

relay clicking away for well over an hour) nothing failed.

Anyway, I've learned a lot about (SMT) fuses, and in particular that the

specification "fast" doesn't say anything, as the I^2t may vary orders of

magnitude among different types of "fast" fuses with the same current

rating.

Thanks once again, best regards,

Richard Rasker

--

http://www.linetec.nl /

http://www.linetec.nl /

Re: Fuse/supply capacitor calculations

How about a Polyswitch self-resetting thermal fuse?

Tyco Electronics makes some of these in a 1206 size. As one example,

their NANOSMDC020F-2 part will sustain a current flow 200 mA

indefinitely, will trip at 420 mA, and works at up to 24 VDC.

Other vendors of polymer self-resetting PTC overcurrent protectors may

have equivalent or similar parts.

--

Friends of Jade Warrior home page: http://www.radagast.org/jade-warrior

Friends of Jade Warrior home page: http://www.radagast.org/jade-warrior

We've slightly trimmed the long signature. Click to see the full one.

Re: Fuse/supply capacitor calculations

I have looked at those, but their popularity (and thus availability) seems

to be waning -- all the types offered by Farnell, for instance, are no

longer in production. But thanks for the suggestion anyway.

Richard Rasker

--

http://www.linetec.nl /

http://www.linetec.nl /

Re: Fuse/supply capacitor calculations

I^2t is proportional to the capacitor's stored energy, 0.5QV^2, so this

theory suggests that the only solution is to reduce the cap size. In

reality, a fuse will pass infinite energy (given a long enough time), so

as you have concluded, one solution is to stretch out the charge time

somehow to get beyond the fuse I^2t region.

Is the device load constant enough that you could put a resistor ahead

of the cap and load? Then, bump up the supply voltage to compensate for

the IR drop. Or place a regulator downstream of the cap.

If you can't put up with the power loss through the resistor, there may

be another way. How is this device powered up? Is it possible to bypass

the fuse and power switch* with a high value resistance that will

pre-charge the cap? The resistor can be selected such that a short to

ground downstream of it will draw a low enough current so that

protecting it with a fuse is not necessary.

*Could be a series MOSFET delayed to power up once the cap voltage has

risen.

--

Paul Hovnanian snipped-for-privacy@hovnanian.com

-----------------------------------------------------------------------

Paul Hovnanian snipped-for-privacy@hovnanian.com

-----------------------------------------------------------------------

We've slightly trimmed the long signature. Click to see the full one.

#### Site Timeline

- » hefty amps-- DC 24-48V @ 1kA supply
- — Next thread in » Electronics Design

- » Question on fusing a car battery
- — Previous thread in » Electronics Design

- » Auction in Fremont, ca NOW
- — Newest thread in » Electronics Design

- » Amateur electronics in danger due to lack of DIP ICs
- — Last Updated thread in » Electronics Design

- » 2,4GHz wifi 4k?
- — The site's Newest Thread. Posted in » Electronics Hobby (Italian)